The wikipedia article on quiet title is also clarifying: https://en.wikipedia.org/wiki/Quiet_title
So is this article on quiet title: http://www.nolo.com/legal-encyclopedia/who-can-claim-propert...
If I understand it right, the issue here is situations like the following. You've got a parcel of land which was 1/2 owned by brother A and 1/2 owned by brother B (due to, e.g., inheritance). Brother A occupied the parcel for 20+ years and eventually sold it to someone else. At this point, according to Hawaii's adverse posession law, brother A owns it but owes compensation to brother B. Now many years later, brother A or his descendents sold to Zuckerberg (or some similar chain of title), and brother B's descendents may not even know they had some right to the land.
There's a theoretical possibility that some descendent of brother B may show up and claim the land.
These quiet title lawsuits are a way for Zuckerberg to pre-emptively settle all such issues. It's also apparently a very common and accepted way to handle such issues in Hawaii.
This is basically just a horrible legal hack around the fact that Hawaii (like many places) has a totally broken title registration system. Without this hack it might be difficult/impossible for a land owner to know with any certainty that they actually own the land they just purchased.
If someone knows more about this, or if my understanding is incorrect, please correct me. I know little beyond what I learned via google.